1. Field of the Invention
The present invention relates to electrostatic generators and motors, and more specifically, it relates to the use of parametric resonance and variable thickness dielectric to improve the performance of such devices.
2. Description of Related Art
Early work (1,2) by Professor John Trump (of M.I.T.) examined theoretically and experimentally a then-new form, of electrostatic generator/motor that was especially suitable for use in a vacuum environment. Subsequent workers (e.g., 3, 4) employed his ideas in their designs. Tramp's generator/motor consisted of interleaving fan-like condenser plates, consisting of “stators” and “rotors.” The stator assembly was supported on insulators, and the rotor “fans” were mounted on a rotating shaft. As the rotor rotated, the capacitance between the stator and rotor would vary between a maximum value, when the blades were directly opposite to each other, to a minimum value when the rotor blades faced the gaps between the stator blades. In many of Trump's generator/motors, “brushes” made contact with the rotor blade shaft to provide a means of electrical connection to the rotor blade assembly. A typical “single-sided” circuit as employed by Trump is shown schematically in FIG. 1 and includes a negative power supply lead 12 connected to ground 10, a positive power supply lead 14 connected to a charging resistor 16, which is connected to the electrostatic generator/motor device 18 which is in parallel to capacitor 20. One side of each of the electrostatic generator/motor device and capacitor are connected to ground 22 and the other side of each is connected on opposite sides of a load 24.
To operate Trump's devices as a generator, a potential was established between the stator and rotor by connecting them to a DC power supply through a high-resistance “charging resistor”. Once the condensers reached the full electrical potential, no further charge was drawn from the power supply. However, when the rotor was spinning, the potential between stator and rotor would have an alternating current component, as a natural consequence of the time variation of the capacitance, as given by the equation;
                                          V            ⁡                          [              t              ]                                =                                    Q              0                                      C              ⁡                              [                t                ]                                                    ,                            [        1        ]            where Q0 (coulombs) is the (fixed) charge on the condenser, and C[t] (farads) is the capacity of the time-varying capacitor. The time-variation of capacity of an actual fan-like capacitor made up of a stationary and a rotating set of sector plates can be modeled reasonably well by the expression:
                                          C            ⁡                          [              t              ]                                =                                    C              0                        ⁡                          (                                                (                                      1                    +                                          k                      ⁢                                                                                          ⁢                                              Cos                        ⁡                                                  [                                                      ω                            ⁢                                                                                                                  ⁢                            t                                                    ]                                                                                                                                      1                  +                  k                                            )                                      ,                                  ⁢                  k          <          1                ,                            [        2        ]            where C0 is the value of the capacity of the condenser at its maximum, and ω is the angular frequency of variation of the capacity as it cycles between its maximum and its minimum value.
Inserting Eq. 2 into Eq. 1, one can calculate the variation in potential for a given set of values for Q0, C0, k, and ω. If we take Q0=V0C[0] as the initial charge (at t=0, a time when the capacity has its maximum value), then we may plot the potential across the capacitor as a function of time (in the absence of any loads connected to its terminals. Such a plot is shown in FIG. 2, for a value of C0=0.1 μfarad, V0=5 kV, ω=2π*(103 Hz), and k=0.6. As can be seen, a large AC component appears, superposed on the DC level The results shown in this plot represent the “driver” for the electrostatic generator/motor. It is desirable to make optimum use (both electrically and geometrically) of this driver in order to maximize the power output of the generator. As will be shown, the special rotor-stator configurations and circuits that are the subject of this disclosure represent a major improvement over the simple configurations studied by Trump and by others following him.